Can someone explain to me in a easy way why is it easier and better to work with Lie algebras than with Lie groups?

I found somewhere that it is difficult with Lie groups because of their global properties which I must admitt do not understand....what does the author mean by saying ''because of the global properties''?

Lie algebras are ''nicer'' because they are vector spaces....but how to interpretate this contribution, in which way the fact that they are vector spaces makes it easier to work with them than with Lie groups instead?

Thank you very much for any help