Definitions of 'Surreder':
1a : to yield to the power, control, or possession of another upon compulsion or demand <surrendered the fort>
1b : to give up completely or agree to forgo especially in favor of another
2a : to give (oneself) up into the power of another especially as a prisoner
2b : to give (oneself) over to something (as an influence)
Mere scholarly definitions.
So in Buddhist terms, what does it mean to surrender?
To me, it may go to the extreme of renounciation, as you surrender everything that you have, to practise and carry on turning the wheel of Dharma with minimal distractions, or like what has been nicely explained on the other posts, to surrender one's mind to the Dharma. From surrendering our mind, our body and speech will transform accordingly; and you are on the path to practising the 8 verses of thought transformation and the 9 attitudes to guru devotion.
Labelling it as 'surrendering to the Dharma', I feel is more pervasive throughout Buddhism, as it encompasses all types and schools of Buddhism.
In Vajrayana, of course, 'surrending to your Guru', is I guess, one of the higher forms of offering you can do, because it shows that you have 100% conviction and faith in your guru. It is the Dharma that your guru brings to you; hence, ultimately you are surrending to the Dharma, but it is the methods in which your guru trains, guides and teaches you that you surrender to him. Whatever that is negatively inert in you, your guru will skillfully exploit that, and use it to train you, so you surrender your negative habituations with hopes of replacing it with positive ones. However, no matter how much we claim that we can surrender, most of us still have resistence. Samsara is suffering.
Yes, it is not easy to surrender, especially in today's society, the age of degenaration (kaligyuya). But I guess you have to stick a feet out and take it step by step - ultimately with resilience and faith, you will succeed and with the guidance of a guru, there's no way but up.