I sometimes see people putting on Tefillin at Mincha time. What is the reason for this? It is because they did not pray with a minyan for Shacharit? Is it obligatory to do so?

The Torah obligation is to put on Tefillin once a day at least for the time of Kriyat Shema. In principal, we should have them on all day, however since people become distracted from the holiness of the Tefillin on them and because we are not able to maintain a level of physical cleanliness which the Tefilllin require, the minhag has become to wear them for Shacharit. (See Shulchan Aruch Orach Chaim 37). On the other hand there is a custom to don Tefillin for Mincha too .(Magen Avraham 37:2) Rav Moshe Feinstein zt"l (Igrot Mosheh 4:34) says though that if it not one's custom it is considered conceit to do so.