As per the SD card specification:
When an SD card is operating in SPI mode or 1-bit SD mode, the CMD and DATA (DAT0 - DAT3) lines of the SD bus must be pulled up by 10 kOhm resistors. Slaves should also have pull-ups on all above-mentioned lines (regardless of whether these lines are connected to the host) in order to prevent SD cards from entering a wrong state.
Basically you need to ensure that "everything is off" until the Arduino actively drives the SD card. Without them the SD card's inputs will be floating and doing anything they like until the Arduino starts communicating.
Resistors in-line with the signals are there really just to increase the impedance and prevent damage when hot-swapping a card.
If you have a 5V Arduino you will require logic level translation. This is a separate thing to the resistors. While resistors are OK for UART or simple IO logic level translation they are not suitable for use with an SD card. This is because the clock frequencies involved are too high and the resistors will corrupt the signal (through low pass filtering). Instead you require an active logic level translation system, such as a dual voltage, or TTL input, buffer, or active MOSFET level shifters.