When a specific person is on the receiving end of a verb, and no other preposition is present, Spanish puts an a in front of them. The literal translation makes no sense, and that is fine.
Espero que vean a María.
The reason is word order. Spanish is flexible about where a name sits, so without the a you cannot tell who is doing and who is being done to.
Espero que comprendas a David · Me gusta que visite a la profesora
Where another preposition is already there, you do not need it: contar con María.
The two words stick together and are written as one.
a + el → al
Al hombre · Quiero que vea al hombre
You always need the personal a when a specific person receives the action, even where nothing is ambiguous. Note "specific": I need to find the plumber takes it, I need to find a plumber does not.
Switching the vowel on ven would give "van", which collides with ir. So the mood tense is built on the irregular "I" form instead, keeping the e.
Espero que vean · Quiero que vea al hombre
Contar is to count, and also to recount, so it works as another verb for to tell, especially with stories. The o splits.
Quiero que me cuentes · Quiero que me cuenten algo · Quiero que cuentes conmigo · Espero que cuentes conmigo · Esperamos que cuenten con María
Another preposition that differs between the languages: English counts on, Spanish counts with.
Add esperar to the list. I hope that is another expression of your subjectivity, so what follows que goes into the mood tense.
Espero que cuentes conmigo · Esperamos que lo cuenten a María · Me gusta que la profesora visite