The SE of the fixed effects are made smaller when the random effect is added because the new implied grouping of term members adds information that wasn’t previously included. This grouping is not implied or encoded in a fixed effects style. It’s additional information that you added. Sometimes folks will say that the improved term “steals” variance from other terms that they shouldn’t have otherwise had.
Gelman and Hill’s book, Data Analysis Using Regression and Multilevel/Hierarchical Models can help.
Also, see this excellent blog post on the topic.