TFA can provide a couple of benefits. First it is a strong (but noncorrosive) acid that can protonate residual silanols on the column and also protonate bases. Second it is a mild ion-pairing agent that can alter the selectivity of basic substances. Third, it can often improve peak shape for bases. Fourth, it is volatile.
It has problems too. It is expensive, especially UV/spectro grades. It causes noisy baselines at low UV wavelengths, even when you buy high-purity grades. It can give strange baseline effects, especially below 230 nm. It suppresses ion formation in electrospray MS. It must be stored carefully or it goes bad. Pure TFA attacks many polymers, including the ones used to make bottle caps.
Many methods specify 0.1% TFA in the mobile phase. This is something of a holdover from days gone by when reversed-phase columns had relatively high residual silanol activity. Modern columns with their lower silanol activity can gain most of the the same benefits with as little as 0.01% TFA.
Often you can substitute phosphoric or sulfuric acid. They have better UV characteristics, and do not ion-pair. Baselines are much nicer. They are nonvolatile. They also suppress electrospray ionization. They are cheap. Not as effective at improving peak shape.
Formic acid is sometimes a substitute. It is not as strong an acid. It is volatile and inexpensive. UV cutoff is similar, but baseline noise and anomalies are usually less. It usually gives much better electrospray ionization. It does not ion-pair. It is less effective at improving peak shape.
Methanesulfonic and perchloric acids are also substitutes, but are less commonly used. Hydrochloric acid is rarely used because it is corrosive to stainless steel HPLC components.
I usually try phosphoric or formic acids first, and only use TFA if the results are not satisfactory. I try to use the least amount that does the job.