*** Added info for the small siphon jet hole ***
1. The water level in the bowl must be at maximum height. Note I said bowl, not tank. This is illustrated in the picture.
How is maximum water level in the bowl achieved? Remove the cover from the tank and look inside. Maximum water level in the "bowl" is achieved by water from the "tank's" fill valve going through a small tubing that is attached to the top of the overflow tube in the tank. When you flush the toilet, you should see a stream of water shooting out of that tubing into the overflow tube as the water in the "tank" is filling. After the tank's flapper closes, that stream of water goes down the overflow tube to fill the water in the "bowl" to maximum height. The duration of that stream of water going down the overflow tube and filling the "bowl" depends on the water level in the tank being high enough. If the water level in the tank is too low, the stream of water will not fill the "bowl" to maximum height. Water level in the "tank" is controlled by the float adjustment in the tank.
If the water in the bowl is not at maximum height when sitting idle, the toilet will not flush properly. To see what the maximum height of the water in the bowl should be, "slowly" pour pitchers of water into the bowl until the water level in the bowl remains the same.
2. Sufficient water must come from the tank to the bowl fast enough to start the siphoning action in the bowl's trap.
When you flush the toilet, water from the tank goes down to the rim in the bowl and then down through the many small holes on the underside of the rim. The holes must NOT be partially clogged, to allow water to flow into the bowl fast enough.
ADDED: The volume and speed of water from the holes in the rim may not flow fast enough to initiate the siphoning action in the toilet's trap. In this case, there will be a small hole (about one inch in diameter) opposing the toilet's trap, right near the word "jet" in the picture. Water from the tank fills the rim to flow from the rim holes and the excess water flows out of this small hole to provide the additional water needed to initiate the siphoning action. This small hole is usually referred to as the "siphon jet".
When sufficient water is flushed into the bowl fast enough, the water is forced through the S trap (indicated as "siphon jet" in the picture) which starts the siphoning action which then evacuates the water in the bowl.
See this web site for more info on how a toilet works:
To test your toilet's bowl and drain system while eliminating the tank and rim holes from the test, do this:
1. Manually fill the bowl to maximum height by slowly pouring pitchers of water into the bowl until the water level does not go any higher.
2. Get a container that can hold 1.5 gallons of water. Dump the 1.5 gallons of water into the bowl quickly.
3. Repeat steps 1 & 2.
4. If the toilet flushes perfectly, then put some toilet paper in the bowl to simulate solid waste. Repeat steps 1, 2 and 4 several times.
5. If the solid waste flushes perfectly, then the problem is in the tank, the rim of the bowl, [ADDED: or blockage of the small siphon jet hole. (The siphon jet hole could be blocked by debris if the toilet was left uninstalled with the tank off and leaves, etc. fell into the drain hole for the tank.)]
If the tests fail, the problem is in your drain or the toilet's trap is probably blocked by a pencil type object.
How many toilets do you have, and do all them have flushing problems or just one?