Actually, if you think about it, it's not just transphobic, it's rooted in a homophobic basis (well, it could be heterophobic if a lesbian called someone a trap).
To expand on ankhtahr's post, from everything I've seen of the term's use... basically, it's claiming that anyone assigned male at birth, presenting as female (whether they identify as female or not), is trying to "trap" straight cis men into having "gay" sex (or lesbian cis women into having "straight" sex, but let's face it, the communities in which "trap" is used, it's all straight cis men), or at least being sexually attracted to someone with genitals typical of a male.
I hope I don't need to explain why that's a rather horrible slur. (Although, it's actually not just transphobic, given that it does affect crossdressers as well, as Rghfrgl points out. But, "transphobic" is probably the easiest category to put it in.)
(Hell, most slurs start out as relatively neutral words, and later get negative meaning assigned to them. This one starts out as negative.)