甚至 (shènzhì) is similar to "even" in English and is used for emphasis. Like "even", it can be used quite directly or in a more subtle manner. When used more subtly it acts to supplement the speaker’s initial thought, creating the impression that the speaker has realized half way through his statement that he hasn’t gone far enough, and wants to take the idea one step further.

Structure
Here 甚至 is used in a more direct manner.
甚至 + focus of emphasis

Examples

tā qí zìxínɡchē de sùdù shènzhì bǐ qìchē hái kuài。
1.他 骑 自行车 的 速度 甚至 比 汽车 还 快。
He rides his bike even faster than cars.

tā shì ɡè tànxiǎnjiā,tā shènzhì qù ɡuò běijí。
2.他 是 个 探险家,他 甚至 去 过 北极。
He is an explorer. He's even been to the North Pole.

zài zhōnɡɡuó,búdàn jiàoyù shuǐpínɡ ɡāo de rén huì bèisònɡ tánɡshī, shènzhì lián xiǎo háizi dōu huì。
3.在 中国,不但 教育 水平 高 的 人 会 背诵 唐诗, 甚至 连 小 孩子 都 会。
In China, not only can well-educated people recite Tang poems, even small children can.

甚至 used for more subtle emphasis

Structure

In this structure, the 甚至 takes things up another degree.
甚至 + supplementary thought

Examples

qián nǚyǒu de zhàopiàn rànɡ tā ɡǎndào yíhàn, shènzhì tònɡkǔ。
1.前 女友 的 照片 让 他 感到 遗憾, 甚至 痛苦。
The picture of his last girlfriend made him feel regret, it even pained him.

wǒ juédé liǎnɡtiān nèi wánchénɡ zhèɡe rènwù hěn nán,shènzhì shì bú kěnénɡ de。
2. 我 觉得 两天 内 完成 这个 任务 很 难,甚至 是 不 可能 的。
I think that finishing this task in two days will be very difficult, maybe even impossible.