Passive parts such as resistors and capacitors have not only a value (in ohms or farads, etc.) but a tolerance which is an indication of how far off that value might be. For example, a nominally 100 Ω resistor with 5% tolerance will not be exactly 100 Ω but should be within 5% of that. In other words, you can expect it to be somewhere between 95 Ω and 105 Ω. If it were 1% it would be between 99 Ω and 101 Ω. Obviously the smaller the tolerance number the “better” in the sense that its value will probably be closer to the nominal value. On the other hand small tolerance parts can be expected to cost more and to be harder to get, and you might not need that precision. But if you have a higher precision (smaller tolerance) part than is specified or necessary, it’ll work fine.
As indicated above, for synth circuits usually 5% resistors are adequate but 1% resistors are only slightly less dirt cheap and can be used almost everywhere, unless the build instructions call for something even more precise (which is rare). In fact if you have a few dozen 1% resistors of the right value, with a multimeter you can probably find several within 0.1% of the nominal value, and using them will be cheaper than buying 0.1% precision resistors.
For obvious reasons, potentiometers don’t have tight tolerances. The value is variable anyway, so it doesn’t really matter much how close to an exact value it is.
Capacitors tend to be lower precision than resistors. ±20% is not uncommon, and you sometimes even find ones with -20%, +80% tolerance — meaning that if it’s nominally 10 nF, it won’t be less than 8 nF, but it might be as high as 18 nF. Correspondingly, circuits usually aren’t designed to require capacitors to be very precise. If the instructions don’t say otherwise, a 20% capacitor will probably work fine. (In fact if you don’t have the right value cap but you do have one that’s within a factor of 2, there’s a good chance you can substitute it with little or no ill effect.)
With semiconductors (diodes, transistors, and ICs) there usually isn’t a single value to quote a tolerance on. If you check the datasheet there might be tolerances given, or min/typical/max values, for several parameters, but there won’t often be higher/lower tolerance versions of the same part. If there are, the circuit diagram or BOM will usually specify which to use — if not, feel free to use whatever’s cheapest or most readily available.