Earlier in common law (England, the U.S, several other places) there was a distinction between suits brought "in law" or "in equity."

Cases which had no remedy under the existing law could be brought as an "equity" claim," in order to achieve a fair result under a situation *where no claim at law existed.*

An example of such a case (to reference your current document) might be where allowing someone to act would cause a type of damage that could not be made up by paying money damages. A court might issue an injunction (an order) in such a case in order to prevent the harm from happening or continuing to happen.

Another equitable remedy is a "constructive trust" where a party can be made to disgorge profit s/he should not have made. A court can actually apply the theory that a person is holding this money "in trust" for someone they've defrauded, in order to get it back.

The law/equity distinction has largely disappeared but will resurface occasionally during technical discussions.

The intent of the passage you cite is to inform the party signing it that they may be subject to equitable remedies in addition to any money damages available.

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Note added at 6 час (2009-02-22 20:06:49 GMT)
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So in sum, you are on the right track.

There is a boilerplate expression "at law or in equity" which can be found in Russian translation as в силу закона или по праву справедливости, thus:

имеющегося у COREL в силу закона или по праву справедливости, включая, без ограничений, любое средство правовой защиты в рамках международных законов об ...
www.shkola.edu.ru/download/EULA/Corel.html

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Note added at 6 час (2009-02-22 20:07:32 GMT)
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использования компания Precor имеет право на судебный запрет, в добавление к другим мерам в силу закона или по праву справедливости. ...
http://eu.precor.com/comm/ru/termsofuse