10 fold cross validation - algorithm

Question

In k fold we have this:
you divide the data into k subsets of
(approximately) equal size. You train the net k times, each time leaving
out one of the subsets from training, but using only the omitted subset to
compute whatever error criterion interests you. If k equals the sample
size, this is called "leave-one-out" cross-validation. "Leave-v-out" is a
more elaborate and expensive version of cross-validation that involves
leaving out all possible subsets of v cases.
what the Term training and testing mean?I can't understand.
would you please tell me some references where I can learn this algorithm with an example?
Train classifier on folds: 2 3 4 5 6 7 8 9 10; Test against fold: 1
Train classifier on folds: 1 3 4 5 6 7 8 9 10; Test against fold: 2
Train classifier on folds: 1 2 4 5 6 7 8 9 10; Test against fold: 3
Train classifier on folds: 1 2 3 5 6 7 8 9 10; Test against fold: 4
Train classifier on folds: 1 2 3 4 6 7 8 9 10; Test against fold: 5
Train classifier on folds: 1 2 3 4 5 7 8 9 10; Test against fold: 6
Train classifier on folds: 1 2 3 4 5 6 8 9 10; Test against fold: 7
Train classifier on folds: 1 2 3 4 5 6 7 9 10; Test against fold: 8
Train classifier on folds: 1 2 3 4 5 6 7 8 10; Test against fold: 9
Train classifier on folds: 1 2 3 4 5 6 7 8 9; Test against fold: 10

Answer 1

In short:
Training is the process of providing feedback to the algorithm in order to adjust the predictive power of the classifier(s) it produces.
Testing is the process of determining the realistic accuracy of the classifier(s) which were produced by the algorithm. During testing, the classifier(s) are given never-before-seen instances of data to do a final confirmation that the classifier's accuracy is not drastically different from that during training.
However, you're missing a key step in the middle: the validation (which is what you're referring to in the 10-fold/k-fold cross validation).
Validation is (usually) performed after each training step and it is performed in order to help determine if the classifier is being overfitted. The validation step does not provide any feedback to the algorithm in order to adjust the classifier, but it helps determine if overfitting is occurring and it signals when the training should be terminated.
Think about the process in the following manner:
1. Train on the training data set.
2. Validate on the validation data set.
if(change in validation accuracy > 0)
3. repeat step 1 and 2
else
3. stop training
4. Test on the testing data set.

Answer 2

In k-fold method, you have to divide the data into k segments, k-1 of them are used for training, while one is left out and used for testing. It is done k times, first time, the first segment is used for testing, and remaining are used for training, then the second segment is used for testing, and remaining are used for training, and so on. It is clear from your example of 10 fold, so it should be simple, read again.
Now about what training is and what testing is:
Training in classification is the part where a classification model is created, using some algorithm, popular algorithms for creating training models are ID3, C4.5 etc.
Testing means to evaluate the classification model by running the model over the test data, and then creating a confusion matrix and then calculating the accuracy and error rate of the model.
In K-fold method, k models are created (as clear from the description above) and the most accurate model for classification is the selected.