Can you grow apple trees from seed?

Yes, it is certainly possible to grow an apple tree from the seeds or pips. However, apples do not grow true from seed, which means the resulting tree will not be the same variety as the variety you got the pips from. Instead it will be a new variety, related to the mother apple that you took the pips from, and the father which supplied the pollen - most likely a crab-apple.

In this respect apples are quite like us - the child is a unique individual, inheriting characteristics from its mother and father (and grand parents and so on).

The seedling trees that you grow from the pips will also take a surprisingly long time to bear new apples, perhaps 8-10 years. And, as mentioned, these will not be Gala apples, they will be a cross between a Gala apple and a crab-apple ... so probably not particularly nice to eat.

In summary, growing apple trees from seed is great fun and very interesting, but if you simply want to grow your own Gala apples (or any other variety) then you need to buy a grafted tree. This is a tree that has been propagated using graft material from an existing Gala apple tree, so the new tree will grow true.