Basically, when one person/party indemnifies another party, that person is saying that if the other party is sued or becomes liable for the first persons actions, he will take responsibly for the the issue and protect that person. In other words, the indemnifying party will become financially responsible for the indemnified party for the instances specified in the indemnity clause.
The fact that the language is mutual, it means that each party will be financially responsible for its acts even if the other party gets sued for them. For example if you injure someone at the wedding while you are taking pictures and the injured person sues the bride and groom because they invited the person to the wedding and hired you, you will be financially responsible because your actions caused the injury. The same would be true if you were taking a picture and lined people up on a riser and the riser collapsed because the bride and groom rented faulty risers. You might be sued as you were taking the picture. The bride and groom would be financially responsible for the bad risers that they rented.
There are other issues with indemnity clauses and particular language within them that are beyond the scope of this answer. It might make sense to speak to an attorney for clarification before you start to use any particular indemnification language.
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A client who has not retained an attorney cannot rely on "advice" but only "analysis". An "indemnify and hold harmless" means that the parties will defend any claim and pay any judgment arising out of the alleged fault of one of the parties. The provision is only good to the extent that the one party actually provides the defense and has the assets necessary to pay such a judgment, if any.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
My colleagues offered very good comments.
Here is an admonition however: just like you would probably think me foolish for wanting to photograph my own events and expect a professional result you should not be serving as your own lawyer when it comes to something as fundamental as your master service agreement.
Not to pick on you, but your question tells us here that you should not be doing this without proper counsel. You should hire an attorney to create the MSA so you have to use for all your clients save for modifications of the service level terms. This should not cost that much and may be critical because we have many photographers as clients and when any provider serves brides and weddings the odds of being sued for something are great... this I bet you know already.
Most of us here offer a free phone consult perhaps now is the right time to build a relationship with a good business lawyer you can work with.
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Michael and Richard both have it right. You are indemnifying the other party and holding them harmless from any loss etc. from your own acts. It may be necessary to have a Contract Law attorney help you design a contract that allows you Alternative Dispute Resolution. Good Luck!