Lo miró un momento y sintió que el corazón se le aceleraba.
She looked at him for a moment and felt her heart speed up.
A couple of notes on grammar.
The indirect object pronoun "le"
The use of the indirect object pronoun (le) here lets us know that it is her heart (el corazón) that sped up. The usage here is very similar to such constructions as "le duele la cabeza/la espalda/el estómago/etc" where the indirect object pronoun indicates to whom the body part belongs.
The detransitizing "se"
Normally, the verb "acelerar" is a transitive verb which means that we should generally expect it to be accompanied by a direct object indicating "what" was accelerated. In such cases, the verb is conjugated so that the subject indicates "who" or "what" caused the acceleration. For example:
?Luisa aceleré el coche al máximo ? Luisa (subject) accelerated the car (direct object) to the limitor less literallyLuisa put the pedal to the metal.
When we wish to say that something accelerates of its own accord, we use the pronominal construction, that is to say that we include the pronoun "se" which acts to detransitize the verb so that we no longer need expect a direct object. We might compare the difference between a transitive and detransitized construction in regards to a heartbeat
Transitive: She sped up her heart.
Detransitized: Her heart sped up.
Hopefully, you see that, of the two, it is the latter that makes more sense in our original context.