The term ‘legal effect’ is used differently colloquially and in legal scholarship. Colloquially, it can perhaps be taken to broadly refer to the effects of law on society, but in law it has a very specific meaning. A few concrete examples will illustrate its meaning in the legal context:
The legal effect of concluding a valid contract usually consists of the attribution of two legal obligations to perform as stipulated in the contract, and two rights to such performance.
E.g. If you conclude a contract of sale to buy a car it has the legal effect of an obligation to pay a price for the buyer and an obligation to transfer ownership for the seller; it entails a right to have ownership of the car transferred for the buyer, and a right to be paid the price of the car for the seller.
The legal effect of stealing a car means that one becomes punishable if the legal conditions for theft are found to be fulfilled by an institution with the authority to do so. This means those convicted can receive the punishments as specified for the offence in the positive law of the jurisdiction in question, except where a justification or excuse applies.