While the degree to which the brain is lateralized is often exaggerated, the other responses to your question are downplaying it too much. One of the most significant aspects of lateralization is in areas of the cortex that regulated language processing. It is generally the case that in most people, the left cortex processes the rules and structure of language, whereas the the right side of the brain processes prosody, which is emotional intonation of language. This lateralization is so pronounced that it manifests as one the most distinct forms of lateralization in the brain, anatomically speaking. Specifically, the planum temporale is in some individuals as much as ten times larger on the left than on the right. This difference was first described in seminal work by Wada et al in 1975 in JAMA.

The degree to which this lateralization exists differs between men and women is not entirely clear. Wada et al and other studies found a sex difference, suggesting that men are more likely to be lateralized than women (i.e. left larger than right), which is part of where this idea that women are more "emotionally centered" in their brains than men. Other studies have not found this difference, however.

A fairly recent study did find a sex difference. Interestingly, they also in men with Klinefelter's syndrome, wherein men have XXY sex chromosomes. These men (I need to be careful here, because some studies have shown the individuals with Klinefelter's syndrome are 10X more likely to be transgender than XY individuals) tend to have female-like breast development and other feminine features. The study above also found that XXY men were not different from women in the degree to which their brains are lateralized.

Anyway, there are other studies showing functional differences in emotional processing of faces between men and women, specifically related to lateralization in the brain. In general, males tend to have a stronger response in the right amygdala than in the left.

The final point I will make is that there is enormous overlap between men's and women's brains. We can find differences in lateralization, size of various things, etc, but the differences are relatively small and not always apparent in every study. Further, you cannot take any one individual brain and make clear judgments about how "male" or "female" it is necessarily. Exceptions always exist.