An effect is something that alters a sound in a specific way. Examples include eq, reverb, delay, wah, phaser, etc. Effects often have parameters that can be changed to customize the way the sound is altered. Examples include repeats for delay, gain for wah, intensity for phaser, etc.
An algorithm is a combination of effects specifically arranged to provide a more custom sound. We make the distinction between effect and algorithm because algorithms often include more than one effect, each having parameters that can be changed. The combinations of these effects and parameters can used to create unique and original sounds that wouldn't otherwise be possible with single effects. Examples include Filter Pong, ModFilter, HarModulator, Reverse Reverb, etc.
A preset is an algorithm saved with its parameters. The H9 comes with presets to give you an idea of what is possible and of course you can create your own. An example would be Bridge of Sighs, which is a preset created using the Digital Delay algorithm. The Digital Delay algorithm combines a stereo delay effect with a modulation effect. Another example is Fra Diavolo, which is a preset created using the CrushStation algorithm. The CrushStation algorithm combines the following effects: overdrive, octave shift, noise gate, compressor and dying battery emulator (sag).