This is a question related to Lo-Rig, the study on valid cognition, 'epistemology'. An authoritative and simple text on the topic is Mind in Tibetan Buddhism, by Lati Rinpoche.
To answer in a practice-oriented fashion: when one is subject to anger (a conceptual consciousness that is also a wrong consciousness in that it engages its object erroneously), one comes to tell himself stories about the object. For instance, one comes to think “This person is detestable; how could have I been fooled and even like her? How could anyone love her? If they knew her for who she is, they would understand; she really wronged me...”. Finding all the more reasons, if not to be angry, at least to justify one's anger. As practitioners we engage in analytical meditation on impermanence & death, karma, refuge, precious human rebirth, and so forth, on a daily basis. It is called “Meditation on the Lam Rim”. We do it for two reasons:
- So as to tell ourselves factually concordant “stories” in order to generate, for instance, patience and dwell in there, familiarizing with being patient, and so forth
- So as to be able to pay attention to facts that we are so often blind to. For instance, after meditating a great deal on buddha-nature, it will be easier to find / see reasons not to despise any sentient beings.
Even when engaging in Calm Abiding, one needs to alternate between (1) analytical meditation and (2) placement, because one has to analyze the object he means to achieve Calm Abiding with in order to (1) familiarize with the object and (2) cultivate the clarity factor with regard to it.
Once our eyes are fully open, once we see reality, there is no need for these anymore. But in our (Geluk, Madhyamika-Prasangika) presentation, only a buddha is free from [the need for] conceptual consciousnesses, and is therefore called 'a valid person'. Also, since even direct perceivers in the continuum of a sentient being are not free from the appearance of true existence, abandoning conception [even the conception of true existence] is not sufficient. That is a unique Tenet of the Prasangika school, though.
To answer in a more technical fashion: a conceptual consciousnesses apprehends its object by way of a mental image (also called 'meaning-generality' or 'generally characterized phenomena'). All conceptual consciousnesses are mistaken [with regard to their appearing object, a mental image] in that they mistake the appearing object for the object of engagement. However, a conceptual consciousness, even mistaken, can be valid. For instance, an inferential cognizer (which is a conceptual) is always valid because it necessarily arises in dependence upon a correct sign that has been realized [and which pervasion in relation to the predicate as well]. This accords with Purbuchok's presentation (in Explanation of the Presentation of Objects and Object-Possessors as well as Awarenesses and Knowers).
We often present the gradual process of generating valid consciousness as follows: Having doubts turning away from the factual [in relation to a slightly hidden phenomena, such as for instance subtle impermanence], one listens to the teachings – listening also comprehends reading – and comes to generate equal doubt. He keeps on listening to the teachings and comes to generate doubt tending towards the factual. He keeps on listening to the teachings, gives it a thought, and comes to generate a correct assumption. Most positions we hold as true without being able to establish by way of reasoning are such. Doubt and correct assumptions are not 'realizing consciousnesses'. Therefore, strictly speaking, someone having generated a correct assumption with regard to a slightly hidden phenomena has not 'realized' anything yet. From there, he engages in reflection and/or in meditation in an analytical fashion and, in dependence on a correct reason, comes to generate an inferential cognizer. That is why we engage so much in debates, familiarizing with reasoning itself, but also with reasons and their pervading such and such predicates (and therefore establishing thesis). An inferential cognizer i is the first realizing (and valid) consciousness in this scenario. It is valid because it engages its object correctly, but it is mistaken with regard to its appearing object, a mental image, because it is a conceptual consciousness. Although a buddha is free from inferential cognition, [valid] inferential cognizers realizing the sixteen aspects of the four noble truths, and so forth are to be cultivated on all the path of learning. It is taught that a slightly hidden phenomena – such as subtle impermanence, and so forth – can be realized directly after having familiarized realizing it inferentially. For instance, subtle impermanence or emptiness are directly realized for the first time in the context of a meditative equipoise (which is a union of calm abiding and special insight) on the path of seeing. Such a realization is preceded by several instances of inferential realization, that is conceptual cognition, also being unions of calm abiding and special insight. A wisdom directly realizing emptiness is not conceptual but is analytical because it is a union of calm abiding and special insight, and special insight has the function of analysis. Only a buddha is free from conceptual consciousnesses.
Wrong consciousnesses (ex.: doubt turning away from the fact, afflictions, etc.), non-realizing conscioussnesses (such as wrong consciousnesses, all types of doubts, inattentive awarenesses, etc.) mistaken consciousnesses (conceptual consciousnesses, including [valid] inferential cognizers) are objects of abandonment. However, they are not to be abandoned by any practitioner. The process of abandonment is gradual... and that which is to be cultivated by one is to be abandoned by another. For instance, inferential cognizers are not to be abandoned by those who still have afflictive obscurations.