Akasha is a term, as well as appearing in Hindu philosophy, appears in Buddhist philosophy.
It is a very interesting concept, mainly because it is one of only three things (dharmas) that is permanent. The other two are forms of extinction of phenomena (pratisamkhyanirodha and apratisamkhyanirodha). It is also one of the six elements, alongside earth, air, fire, water and consciousness.
To be permanent, something has to be uncreated - because all things that are created from causes and conditions eventually change in some way, so the original no longer is in existence. Since space as defined here is not a created thing, is is not subject to cessation.
But what is akasha? Basically, it is space. But there are two kinds of space to be considered in Buddhist philosophy, one permanent, the other impermanent. The impermanent form of space is that create by cavities or partitions, for example the rooms of house, or even the cardinal directions. Any kind of partitioned space or volume is impermanent, since when the partitions are removed, the space can no longer be found to be in existence since it was only known by reference to the material or conceptual parts that define it – it is therefore something that is conditioned. This is not akasha, though. Because of how it is defined, it is not a 'thing', unlike a cavity.
Akasha has a definition of 'that which does not hinder'. It is essentially the fact that there is the possibility of 'somewhere' for things to exist in, and in this way it exists only as a negative definition. It has no positive qualities - even no positive existence. But of course if it did not exist, then there would be no absence of obstruction, so there would be no possibility of objects existing in the universe, since there would be nowhere for them to exist.
Space in this definition is a frequent synonym in Mahayana Buddhism and in Tantra for the empty nature of phenomena, and for the ultimate nature of the mind itself. Padmasambhava says it beautifully when he teaches "sentient beings and their defilements are like knots tied in space", that is to say beings and other phenomena are 'clearly apparent non-existents' - when analysed using Madhyamaka reasoning, phenomena are not found to exist, nor are they found to be non-existent - or any combination of these two facts (the addition of both, or the negation of both). They are ultimately like a mirage or a dream. The contemplation of akasha can therefore be conducive to the contemplation of the mind (as echoed by the famous statement "none of the Buddhas of the three times have ever found their mind") and emptiness, which is the means by which complete the enlightenment of a Buddha is achieved.