Liquid fertilizer is plant food dissolved in water rather than carried into the soil on a solid grain. That one difference explains both why it works faster and why it is easier to get wrong. A dissolved feed is available to the root surface and the leaf immediately; a granular one has to wet, break down and diffuse before the plant sees any of it.
Where a liquid feed is worth the trouble
Because it acts quickly, liquid feeding is the right tool at the moments when a plant needs something now: at the start of a growth flush, at bud formation, or when a shortage has just been identified and the leaves are still worth saving. It spreads evenly through a pot, so no single point receives the concentrated salt deposit that a handful of granules pressed against a root will create. Plants with shallow or already-damaged roots benefit from that most of all.
It is not a substitute for a slow base dressing. A pot that has been standing for a year needs organic matter and structure, not another drink of fertilizer water, and a liquid feed will not rebuild either.
Five ways to apply it
Foliar spraying is the fastest route and the most efficient per unit of fertilizer used, since the leaf takes the solution directly. It should be done in the early evening or on a cloudy day. A spray that dries on the leaf in strong sun concentrates down into the range that scorches, and the damage is visible as burnt edges within a week.
Seed soaking wets the coat and gets nutrients into the embryo before sowing, which lifts germination on tired or old seed. Drip feeding puts the fertilizer into the irrigation line so water and food arrive together in measured amounts, and it is the version that keeps a covered or plastic-mulched bed fed without anyone reaching into it. Straight drenching is the same idea done with a watering can: dissolve, pour, and let the drainage hole confirm the mix went through the profile instead of sitting on the surface. For soilless culture a liquid feed is not a choice but a requirement, because there is no soil reservoir to draw on at all.
The one rule that matters
Concentration, and nothing else. Fertilizer in solution touches the whole root surface at once, so an over-strong mix damages the plant everywhere rather than at one spot. The honest version of the old advice is simply this: never let strong fertilizer sit on plant tissue, and measure the ratio of fertilizer to water rather than judging it by eye. Feed weak and often, water plain once a month to flush accumulated salts, and never feed a plant that is dry at the root or checked by heat, since it cannot move the solution away from its roots.
The other thing worth saying is what a liquid feed does not do. It will not improve the structure of an old, settled compost, it will not restore drainage to a pot that has gone compact, and it will not make up for a missing base dressing. Dissolved trace elements are a genuine advantage of the method, and even distribution is a real one, but a tired potted plant usually needs fresh material and a smaller pot rather than more fertilizer water.
What to dissolve, how strong and how often is worked through at feeding potted plants. The household materials worth putting in a barrel are assessed in kitchen fertilizers, and the shortage you are trying to correct is identified at reading a yellow leaf.