Children develop skills at different rates, but by 3 years children usually:

Listen to and understand a simple story with pictures, although they can still get easily distracted.
Understand lots of words, at least 300.
Understand longer instructions, such as ‘make teddy jump’ or ‘put daddy’s cup on the table’.
Understand simple ‘who’, ‘what’ and ‘where’ questions.
Understand the words ‘big and ‘little’.
Put 4 or 5 words together to make short sentences, such as ‘he took my ball’. Ask lots of questions.
Use action words such as ‘run’ and ‘fall’ as well as words for the names of things.
Start to add ‘s’ to words to show there is more than one of something e.g. ‘shoes’.
Can say the sounds p, b, t, d, m, n, w, k and g in words when they are talking. They may still make mistakes with how they say words, and might have difficulty saying more complicated sounds like sh, ch, th and r. However, people who know the child can mostly understand them.
Start to be interested in other children’s play and want to join in.
Start to talk about themselves, e.g. they can say what they like and don’t like.
Answer simple questions about objects, for example ‘which one do we eat with?"

Things to look out for:

Some children struggle with learning to talk and understand words. Possible signs to look at for at this age include:

Your child points or shows what they want rather than saying it.
Your child only says single words instead of joining words together into short sentences.
Your child has difficulty understanding your instructions and needs you to show them instead.
You cannot understand most of what your child says.