For an attorney, in the ethical rules of conduct, there are three broad areas of conflict. Two of these areas of conflict are between clients, with the other conflict being with the attorney themselves.
The first conflict tends to be in the representation of multiple parties. For example, say two individuals were charged with defacing someone else's property. A defense attorney cannot represent both individuals, because the best defense may be to say it was all the other person. This is a limitation on the ability of attorney to represent their clients and is forbidden. Another example, is an attorney should not represent a company and one of the founding members, for much of the same reasons.
The second type of conflict is similar in concept, the primary difference is temporal. In the first conflict type, both clients, with contrary interests, were in the office at the same time looking for the same person to represent them. In this second type of conflict there is time between the two potential clients. This tends to be dealing with matters which are different, though with over lap. For example, an attorney crafts a settlement agreement between Jordan and Clair, on behalf of Clair. A year or two later, Jordan approaches the attorney to find a way out of the settlement agreement. If the attorney did so, he would be undoing work he had previously done. Thus, this is the second type of conflict.
The final type of conflict is when an attorney and a client have a relationship beyond a professional one. Do the two try to go into business together? Is the client the attorney’s mother, with the client seeking a will where the attorney is going to be a beneficiary? Is there a sexual relationship? Is there a loan between the two? Any of these can put the personal interests of the attorney against the professional responsibilities of the attorney and therefore being a conflict of interests.
Keep in mind the attorney you go to speak with should run a conflicts check. If they don’t there can be problems down the line for you, the client. For example, the opposing side could try to have your attorney removed. It is in your best interest to find the right attorney, not just the perceived best attorney.