Barristers and solicitors are all lawyers, but they are different types of lawyers. One is not 'better', more experienced or more senior than the other. They have quite different training and expertise and do different types of legal work. The system that operates in England & Wales is a 'split' system, where there is a division of labour between these two types of lawyers. In some countries (such as America) there is a a 'fused' system where all lawyers can (potentially) do all things, although of course they will tend to specialise.
Barristers are self employed. solicitors are not. they are employed or partners. Barristers aren't allowed to form partnerships or companies, they trade as sole traders, but group together for economy and marketing under one roof which is called a 'chambers'.
Because barristers within one chambers are all independent from one another they can act on different sides in the same dispute, but solicitors in the same firm can't because they aren't independent and would have a conflict of interests.
Barristers are specialist advocates or specialists in a particular area of law (or both). solicitors do also specialise, and some do their own advocacy, but most solicitors are primarily litigators. this means meeting the client, working out what the case is, sorting out the paperwork, communicating with the other sides' solicitors and where necessary instructing a barrister to advise about the law or to go to court and represent the client on their behalf.
Barristers spend a lot of their time in court, talking to other barristers, dealing with witnesses giving evidence and addressing the Judge. Solicitors often come to court to support a barrister by taking a note or having the files to hand incase the barrister needs something. Increasingly often a barrister attends court without a solicitor. This is often more cost effective.
A barrister is often paid by the piece of work, i.e. £x to attend for this hearing and £y to draft this document. A solicitor usually bills by the hour. Barristers are usually sent to court because its cheaper than sending a solicitor who bills by the hour or because the barrister is more experienced at dealing with the court side of the process (or both).
A client can instruct a solicitor directly but to instruct a barrister you have to first instruct a solicitor as intermediary and they will instruct a barrister for you. Recently a new scheme has been introduced where a client can instruct a barrister direct through a scheme called 'public access' but this is only in certain types of cases and only where the client can effectively act as their own solicitor.
A barrister will often but not always deal with a case all the way through. However because a barrister is usually briefed each time a specific piece of work needs to be done (a hearing, a piece of drafting) there might be different barristers dealing with a case, although the solicitor will remain responsible the whole way through. This is because a solicitor is retained by a client and is responsible for dealing with what comes up as it comes up, but a barrister cannot always be available for a client to attend a particular hearing because these dates are not known at the outset. If a barrister has been previously booked to do something else for another client on the date in question she will have to honour that committment. This called the 'cab rank rule' and it is what helps keep barristers independent by preventing them from picking and choosing the cases they want to do unfairly.
Contrary to popular belief both barrsiters and solicitors can become judges, although more judges have come from the bar than from the ranks of solicitors, and still do.
As with everything - the points above are not true all of the time, but they are generally applicable