Solfege is a system that musicians (mainly singers) use to sing a phrase of passage if there are no lyrics or words written, it's mostly used as an exercise and it can seem unclear what the benefit is when initially using it.
They are monosyllabic words that were originally French. each word corresponds to a note of the musical scale (major, minor, etc) and changes in context of the music sometimes. In a major scale the solfege is Do (1 root), Re (2), Mi (3), Fa (4), Sol (5), La (6), Ti (7). The numbers denote the notes relation to the root.
Essentially it is another way to denote where the note is in relation to the key/scale/chord.
So if that is it why don't people just use 1,2,3 to say where the note is? Because ALL solfege is one syllable (monosyllabic) and so you don't have to end up singing like "SEVEN, SIX, TWO" but instead "Ti, La, Re" it just sounds nicer and you won't even have to worry about identifying accidentals because each accidental will have it's own solfege letter assigned!
On top of that your ability to recognize notes and chords/chord functions will develop quite quickly with regular practice. It sort of gives you a musical super power.
I hope this helps!