Pronominal verbs, often (misleadingly) called reflexive verbs, are verbs in which a "pronoun" clitic is inserted that agrees with the subject. The term reflexive is often used to cover all these verbs, because a helpful notion for understanding them is that "the object of the verb is the same thing/person as the subject", as in English he washed himself. However, there are cases such as reírse where this analysis is less clear. So strictly speaking, reflexive verbs can be seen as a subset of pronominal verbs.
The infinitive of pronominal verbs has the clitic se added to the end: lavarse, bañarse, esconderse, hartarse etc.
Here is the verb bañarse, to have a bath/shower, conjugated in the present tense:
Note that the clitic "agrees" with the subject, even though that subject may not actually be expressed. For example, in me baño, the clitic me (=myself) "agrees with" the subject yo, although this subject isn't explicitly expressed.
With pronominal verbs, the clitic follos the word placement rules of clitics in general. In continuous forms, the clitic can be attached to the participle (ending in -ando/-endo) or come before the form of estar. So either se está bañando or está bañándose is possible. In compound tenses such as the perfect, placing the clitic before the form of haber is more common (me he bañado rather than ?he bañádome).
Types of pronominal verb
Pronominal verbs fall into various categories:
1. These verbs can often be identified (at least by native Spanish speakers!) by seeing if it's possible to paraphrase them with a construction involving a sí mismo. For example, se lavó could be (emphatically) paraphrased as se lavó a sí mismo.