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I have a plan to present my research at the University of Bristol between 10-16 July 2016. I am a lecturer in Government University in Thailand. My wife also applied for a Standard Visitor visa. She would like to have a vacation while I am staying in Bristol. My wife does not have a full-time job but is currently working as a part-time tutor for high school students. She attached a picture of her class, marriage certification and bank statement of my deposit account. Everything should not be a big trouble because her passport has a record of five Schengen visas (Germany and France) in the last two years.

Today she was refused a UK visa. The reason given that the picture of her class is not reliable. They did not believe that my wife will intend to leave UK after five days! We already paid for flight, accommodation and local transportation.

I don't know what to do next. I truly do not understand the reason for refusal.

Should I reapply again and is so what documents do I need to add?

First, the basic idea is that they want to see evidence of your ties to Thailand to indicate that you plan to return after your visit. Evidence of your employment, income, and savings are important parts of that process.

The main evidence your wife appears to have submitted was in the form of photographs. Photos are generally poor evidence, because anybody can take a picture of themselves in front of students. A picture of your wife in front of a class tells them nothing other than that she posed for a picture. It is not useful proof of anything. The UK government has a document that details the types of supporting documents you might submit with a visitor visa application. You should read this guidance carefully. Section 4 lists "documents you should not send unless specifically requested" and includes "photographs (other than passport photographs required in section 1" in that list. If you send photographs, the visa officers will conclude that you haven't read the instructions carefully, and that will hurt your chances of success.

So what do they want to see? First, financial documents, such as bank statements. We have an excellent answer over here that will tell you all about submitting bank statements with a UK visa application and what they say about you.

Next, they want to see "details of employment or studies." This would normally be a letter on company letterhead "detailing your role, salary and length of employment." Paystubs might be helpful too. She indicated on her application that she also works in a cafeteria; she should have proof of this in the form of these types of documents.

Self-employment is more tricky. They ask for "business registration documents confirming the business owner’s name and the date the business started trading." She should have records for her business, even if the business is not subject to tax.

And most importantly, all the pieces of the puzzle should fit together. The letter from her cafeteria job should say she is paid X/month, and X/month should appear monthly in her bank statements. The records from the tutoring business should indicate a certain income (even if it varies from month to month) and that income should appear as deposits in the bank statements. All that income together should match up with the income she states on her visa application.

Finally, as noted in the comments, you should never purchase non-refundable tickets before you have a UK visa in hand.

Adding a small note to Zach's excellent answer, your wife was refused under Appendix V

APPENDIX V:

Immigration Rules for visitors Introduction A visitor is a
person who is coming to the UK, usually for up to six months, for a
temporary purpose, for example as a tourist, to visit friends or
family or to carry out a business activity.

section 4.2

V 4.2 The applicant must satisfy the decision maker that they are a
genuine visitor. This means that the applicant:

4.2(a)

(a) will leave the UK at the end of their visit;

This requires showing that the applicant has ties to their home country that strongly indicate they intend to return home.

and 4.2(c)

(c) is genuinely seeking entry for a purpose that is permitted by the
visitor routes (these are listed in Appendices 3, 4 and 5);

And the relevent portion from Appendix 3

Tourism and leisure

3 A visitor may visit friends and family and / or
come to the UK for a holiday.

This requires showing the applicant has sufficient funds for their intended purpose of tourism. If the person cannot afford to travel themselves, they must show evidence of a sponsor who will be providing for them and has the resources to do so.

Further useful information can be found in this post.