The cycles setting tells DOSBox how many emulated CPU instructions to (attempt to) process per second. Generally a lower number will make games run as they would on a slower real CPU and a higher number would make them behave as if they were running on a faster real CPU. If you set the cycles value too high, however, your real CPU may not be fast enough to comply, and DOSBox may start sacrificing accurate emulation of things like sound in order to try to keep up.
cycles=max will make DOSBox automatically and continually adjust the cycle count to be as high as it can without starving itself of resources needed to do things other than just CPU emulation.
cycles=max limit somenumber is similar, except that it will not go higher than the specified limit (good for games like Daggerfall that need a good amount of cycles but that get flaky at super high CPU speeds). This option wasn't well documented in DOSBox's readme.txt last time I checked.
The core setting tells DOSBox which method of CPU emulation you'd like it to use. core=normal will emulate every CPU instruction purely in software, which is very stable and portable but can be slow. This setting is recommended for older DOS games because of the greater stability and because they tend to be more sensitive to speed issues.
core=dynamic tells DOSBox to use a technique called dynamic recompilation to try to speed things up, but note that it can cause stability issues in some games and may be supported on some systems. This setting is highly recommended for later DOS games because they tend to be more demanding in terms of CPU requirements.
core=auto will let DOSBox try to choose either normal or dynamic. With this setting DOSBox will generally use normal unless it detects that a game is running in 32-bit protected mode, since many later DOS games work that way.