What is the exact difference in Buddhist meditation and meditation in other religions.
One of the key aspects of meditation in Buddhism is that there are, very broadly**, two different kinds (or styles or methods or purposes or ...). One kind is intended to train the person's ability to focus their attention, and to calm their mind. That kind is called samatha (or shamatha) meditation; its aim being various forms of samadhi. The aim of the other kind of meditation is to gain insight into -- that is, to understand and experience -- the fundamental nature of reality, specifically the three characteristics -- i.e. that, contrary to the normal view reality: is impermanent, does not provide freedom from suffering, and does not contain any specific permanent thing that we can call "self". This form of meditation and its aim have the same name -- vipassana.
The first of those two kinds is not specific to Buddhism, and can be found throughout Hinduism and other religions. Buddhism's unique offering to the world is the second kind, Vipassana. That said, it's not clear that it's entirely unique to Buddhism in the sense that there are practitioners of other religions who appear to have achieved the outcomes that vipassana is intended to achieve. For example, it's arguable that St Teresa of Avila, a Catholic Christian nun, was describing stream entry (one of the major attainments in vipassana meditation) in her seventh mansion in her "The Interior Castle". Of course that may be because Christianity, especially contemplative/mystical Christianity, was being influenced by the earlier Buddhism. Regardless, the point is that in practice a style of contemplation (meditation, prayer, etc) leading to fundamental insight does exist today outside of Buddhism.
** It can be argued that there aren't two different kinds at all, but in typical "western" discussions, that's how it's spoken of. It's not, as far as I can see, a gross error to speak of it like that.
The main difference would be the goal. In Buddhism this is done to develop wisdom and mastery over the mind. But in other systems it can be to get a pleasant experience, concentration, psychic powers, etc.
Some of the meditation instruction in Buddhism are ones that were already there but refocused and modified towards gaining wisdom in the process.
I will try to give you a simple answer without talking about higher states of mind, Vipassana and Jhanas: Meditation in Buddhism can enable lots of incredible things for advanced meditators.
Meditation in Buddhism, let's say for beginners, is a very important tool to help us with the following points:
Tranquility / Understanding of the Buddha's teachings / Contemplation / Insight / Understanding of feelings, body and mind / etc..
Lots of people use meditation for well being, tranquility and health benefits.There is nothing wrong with that, but Buddhists use it as a very important tool for a higher goal.